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C₂⁶×H(5,𝔽₂) #72291317

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

241541800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 10 generators on 20 points:

(13,14)(15,20)(16,18)(17,19);(13,15,17,16)(14,18,19,20);(3,4);(13,14)(15,18)(16,20)(17,19);(13,16,17,15)(14,18,19,20);(5,6);(7,8);(9,10);(11,12);(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((13,14)(15,20)(16,18)(17,19), (13,15,17,16)(14,18,19,20), (3,4), (13,14)(15,18)(16,20)(17,19), (13,16,17,15)(14,18,19,20), (5,6), (7,8), (9,10), (11,12), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12));